In MCA models, particular in those cases where the individual and group level models are identical, is there any reason to expect the factor loadings for the group level model to be largers than those found in the individual level model?

Between-level loadings and R-squares (reliabilities) are often larger than within counterparts. This relates to classic literature on ecological correlations (Robinson, 1950, Am Soc Rev), and may be thought of as a reflection of the fact that between-level error variance is smaller due to considering outcomes aggregated to the cluster level where errors tend to cancel out. For more references, see multilevel factor analysis in my 1989 Psychometrika paper.

I am looking for guidance on how to conduct a multi-level factor analysis using Mplus (which I do not own yet and am considering acquiring). I have read the 1991 Muthen "Multilevel Factor Analysis of Class and Student Achievement Components" paper and would like to know how to actually obtain the types of results that are reported and discussed in this paper. I am working with a data-base that contains survey responses from 1,500 persons who represent 72 local welfare offices and I want to create scales that characterterize the organizational conditions in these offices using the survey responses.

I believe the example Cont10 under Examples Using Mplus on this website is close to what you want to do. It is a one-factor multi-level model with covariates. It can be generalized to a multi-factor model.

I have been attempting to conduct a multilevel factor analysis and am having no luck at all getting loadings. I have attempted to model both the within and between, then I attempted to do it with no model statement. I have even attempted to model almost exactly the model that you have represented in Muthen 1994. I conceived of the between portion of the measured variables as latents and included them in my model statement for between. However, I cannot get any loadings at all, and am afraid that I am making the process much harder than necessary.

BASICALLY, I am attempting to get loadings for three levels: the links between the latent variable "WITHIN" and the measured indicators; the links between the measured indicators and the latent "between" portions of each; and the links between those latent "between" portions of the measured variables and the latent variable "BETWEEN". But I am not having much luck. My next step will be to utilize the "BETWEEN" and "WITHIN" portions as predictors of another continuous latent variable measured by its own indicators.

Note that Mplus automatically produces latent variable for the between portion of each variable measured on the individual level, so there is no need to create those. Having said that, it is difficult to give general guidelines for this analysis and in this case it is probably easier if you email the input, output and data to Mplus suport.

Hi, Thank you. Is the reliability formula in the-two level design the same as in the single level? In other words, we can use alpha or composite reliability to estimate test reliability in the-two level design. Thank you.